If " C " is a symmetric conference matrix of order " n " > 1, then not only must " n " be congruent to 2 ( mod 4 ) but also " n " & minus; 1 must be a sum of two square integers; there is a clever proof by elementary matrix theory in van Lint and Seidel.
12.
The argument for n \ geq 2 is similar to the n = 1 case, only one replaces Tietze moves for the fundamental group presentation by elementary matrix operations for the presentation matrices for H _ n ( X; \ mathbb Z ) ( using the presentation matrices coming from cellular homology . i . e . : one can similarly realize elementary matrix operations by a sequence of addition / removal of cells or suitable homotopies of the attaching maps.
13.
The argument for n \ geq 2 is similar to the n = 1 case, only one replaces Tietze moves for the fundamental group presentation by elementary matrix operations for the presentation matrices for H _ n ( X; \ mathbb Z ) ( using the presentation matrices coming from cellular homology . i . e . : one can similarly realize elementary matrix operations by a sequence of addition / removal of cells or suitable homotopies of the attaching maps.
